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The relationship among the entanglement creation within coherently pumped andclosely spaced two-level emitters longitudinally coupled with a single-modeboson field, and the subsequent quantum cooling of the boson mode isinvestigated. Even though the two-level qubits are resonantly driven, we havedemonstrated an efficient cooling mechanism well below limits imposed by thethermal background. Furthermore, the cooling effect is accompanied byentanglement of the qubit pair components when the dipole-dipole frequencyshift is close to the frequency of the boson mode. The maximum boson modecooling efficiency realizes on the expense of the entanglement creation.Importantly, this occurs for rather weak external pumping fields protecting thesample from the deteriorations. Finally, the conditions to effectively optimizethese effects are described as well.

Entanglement versus cooling in the system of a driven pair of two-level qubits longitudinally coupled with a boson mode field